A twin-clutch transmission speed change control device such as the one disclosed in Japanese Laid-Open Patent Publication No. 2006-194405 has been proposed in the past as a speed change control device of a transmission for a vehicle. In this type of speed change control device, pre-shifting is performed prior to switching from the current speed step that belongs to one speed step group to a target speed step that belongs to another speed step group. The term “pre-shifting” refers to an operation whereby a speed-change shaft that is not coupled to an input shaft among two speed-change shafts, and a target speed-change step gear that corresponds to a target speed-change step, are coupled using a coupling mechanism prior to switching of the speed-change step, allowing the time lag that occurs during switching of the speed-change step to be reduced. When, for example, the speed-change step is switched from a second speed to a third speed, one speed-change shaft is coupled with the input shaft and the speed-change step gear of the second speed, and the vehicle travels at the second speed. During this process, the coupling mechanism moves from the neutral position toward the speed-change step gear of the third speed, and a gear provided to the coupling mechanism meshes with a coupling gear provided to the speed-change step, whereby the other speed-change shaft that is not coupled with the input shaft is coupled with the speed-change step gear of the third speed. The speed-change shaft coupled with the speed-change step gear of the second speed is then released from the input shaft, and the speed-change shaft coupled with the speed-change step gear of the third speed is coupled with the input shaft, whereby the speed step is switched from the second speed to the third speed.